On Thursday morning, the budget-cutting Reagan administration will begin paying an additional million dollars a day to the country's milk producers, a special interest group that supposedly lost out in every congressional vote on milk this year.

The increased subsidy will have to be paid because the existing farm program expires at 12:01 a.m. Thursday, and Congress has failed to adopt a new one. As a result, dairy price supports will have to be paid according to the Agriculture Act of 1949 at a rate of 75 percent of parity. That will mean raising the current support 3.5 percent, from $13.10 to $13.56 per hundredweight of liquid milk.

The administration is hoping there won't be too many of these million-dollar days, because Congress will be able to cut them off soon--before the end of October--if it acts relatively efficiently. But even if the drain on the Treasury is held to $20 million or $30 million, it will be an embarrassment to the cost-cutting White House.

This happened because the Reagan administration could not get ahead of a crowded congressional calendar--and apparently didn't realize that it was falling behind. As recently as last week, Agriculture Secretary John R. Block expressed unqualified confidence that Congress would pass new farm legislation in time to head off these million-dollar paydays for the U.S. dairy industry, which already stands to collect nearly $2 billion in government subsidies this year.

The administration-backed farm program, which the Senate has adopted andwhich has good prospects in the House, would permit the secretary of agriculture to bring the support level back to $13.10. Vote counters in the House expect this provision to pass.

But before the House can act, there will be chaos in the nation's dairy markets. "This will be very confusing," said Patrick B. Healy, secretary of the National Milk Producers Federation. "Certainly there will be market disruption for a couple of weeks," said an Agriculture Department official. (No other commodity will be immediately affected by the lapse in farm legislation.)

Processors of butter, cheese and nonfat dry milk--dairy products the government must buy at support prices under the law--will rush their goods to market after Oct. 1 while the price remains high.

Stocks of these products now held in private hands will disappear into government-leased warehouses, which are already groaning with hundreds of millions of pounds of surplus dairy products.

Consumer prices will go up too, probably at least as much as the 3.5 percent that the price support will rise. Ellen Haas of the Community Nutrition Institute, a consumer group, predicted that prices are unlikely to fall back later if and when the government price support returns to $13.10.

Healy of the Milk Producers Federation said he doubted dairy farmers would receive much if any of the increased price support if it only remains in place for a few weeks. He said the processors would be able to keep the extra money, since farmers have to sell their milk every day, and in the current milk glut it is a buyers' market. (However, many dairy processors are farmer-owned cooperatives.)

Healy was a party to the Reagan administration's hurried and unsuccessful effort to avoid this million-dollar-a-day drain on the Treasury.

Last Thursday, the Agriculture Department realized that the House was not going to enact a farm bill by Oct. 1, despite earlier hopes that it would quickly accept the Senate bill. Even the Republicans on the House Agriculture Committee opposed this idea.

Department officials then proposed to Sen. Jesse Helms (R-N.C.), chairman of the Senate Agriculture Committee, that he offer a rider on the Senate floor to head off the increase in dairy price supports. Helms agreed to offer this rider as an amendment to the "continuing resolution" that Congress must enact before Thursday to keep the government operating. (Like the farm bill, all the appropriations bills that finance government activities expire on Oct. 1.)

But a rider on dairy supports could be blocked by a single senator's objection on the floor if it were not "germane" to the continuing resolution. And Sen. William Proxmire (D-Wis.), a fervent friend of the dairy industry, was on the floor Thursday night ready to object to Helms' rider.

The administration approached Healy to see if some deal could be worked out, but those negotiations failed. Friday, the Senate passed a continuing resolution with no mention of the dairy program.